Time‐space decomposition of the transient pressure field generated by a rectangular piston

Abstract

Exact solutions to the acoustic wave equation for canonical geometries are important for transducer evaluation and as a reference for large‐scale simulations of wave propagation. An exact solution for the transient pressure field generated by a rectangular piston is derived. Consisting of a superposition of integrals, this solution avoids the edge singularities associated with earlier solutions. Computational overhead is significantly reduced by applying a novel time‐space decomposition technique, whereby the spatial and temporal dependence of the integrand is analytically separated. By evaluating a set of integrals at each point in space, the transient pressure field is synthesized by weighting and summing against a set of time‐dependent functions. This decomposition technique, which utilizes spatially band‐limited integrands, avoids the artificially large sampling frequencies associated with the standard impulse response approach. Quantitative comparison with the spatial impulse response method is made in terms of maximum error and computation times. At 10% peak error, the time‐space decomposition technique achieves a factor of 2 speed‐up compared to spatial impulse response. Due to the rapid convergence of the integrals in the new technique, the speed‐up increases to a factor of 6.8 at 1% peak error. [Work partially supported by NIH Grant 1R01 CA093669.]